Rate Dependent Material Properties of an OFHC copper Film (Dynamic Behavior of Materials)

ABSTRACT

The material properties of OFHC(Oxygen Free High thermal Conductivity) film with a thickness of 0.1 mm was evaluated at the strain-rates ranging from 0.001/s to 500/s using High-Speed Material Micro-Testing Machine(HSMMTM). The high strain-rate material properties of thin films are important especially for evaluation of structural reliability of micro-formed parts and MEMS products. The high strain-rate material testing methods of thin films, however, are not yet thoroughly established while testing methods of larger specimens for electronics, auto-body, train, ship and ocean structures has been well-established. For evaluation, a HSMMTM has been newly developed to conduct high-speed tensile tests of thin films. The machine developed has a capacity of sufficiently high tensile speed with an electromagnetic actuator, a novel gripping mechanism and an accurate load measurement system. The OFHC copper film shows high strain-rate sensitivity in terms of the flow stress, the fracture elongation and strain hardening. They increase as the tensile strain-rate increases. The quantitative comparison would provide material data at high strain-rates for design and analysis of micro-appliances and micro-equipments.

INTRODUCTION

Investigations of the mechanical properties of thin films for micro-parts and MEMS products have increased in researchers of these products over the past decades. In recent years, a variety of micro-parts, such as micro-levers, micro-connectors, micro-screws and springs, have been developed. These parts require high reliability and good dimensional accuracy and productivity. The high strain-rate material properties of various materials for micro-parts and MEMS applications are required to design and evaluate the product quality and performance levels during the processes of high-speed forming and impact loading, the latter of which induces high strain-rate deformation of many different materials. Micro-forming processes generally demand a high production rate[1-2] which causes high strain-rate deformation as these processes proceed. Thus, the high strain-rate material properties of small-sized materials are required to analyze the high-speed micro-forming process accurately. Sharpe[3] pointed out two important factors in the testing of new materials on a microscale. First, the specimens must be similar in size to structural components. Secondly, the specimens must be produced by the same manufacturing processes used for the components. Therefore, a new material testing technique valid at high strain-rates is necessary for microscale specimens. Material testing results for various specimens [4-16] according to their cross-sectional areas and strain-rates are shown in Fig. 1. Material tests at various strain-rates have been performed by many researchers in accordance with the specimen size in relation to the size of the structural component. Material testing methods to obtain a stress-strain relationship generally differ depending on the strain-rate. General mechanical or hydraulic machines, such as the Instron UTM, are used to obtain the stress-strain relationship at a low strain-rate of less than 0.1/s. The material properties at intermediate strain-rates ranges ranging from 1/s to 1000/s were obtained using high-speed material testing machines with a servo-hydraulic type actuator[16-18]. A split-Hopkinson pressure bar apparatus, also known as a Kolsky bar, is a popular type of experimental equipment used for the identification of dynamic material characteristics at high strain-rates ranging from 103/s to 104/s[19]. For small-sized specimens, material tests using mechanical[20], piezoelectric[14, 21] or electro-magnetic actuators[9-12] are commonly conducted at quasi-static strain-rates of less than 10-2/s. The tensile testing method for thin-film materials has become well established over the past few decades. However, high-speed material testing techniques for small-sized specimens are not yet established owing to the delicacy inherent in the testing methods and the difficulty in specimen handling. In contrast, high-speed material testing techniques for various materials of common sizes, such as conventional auto-body steel sheets, different types of copper, aluminum alloys and polymeric materials are well developed. The present paper suggests a novel high-speed material micro-testing technique at microscale and investigates the high strain-rate material properties of an OFHC copper film. The material properties obtained are compared to those of a bulk OFHC copper sheet in terms of the rate-dependent flow stress curve, strain-rate sensitivity, strain hardening and fracture elongation. The tensile material properties are indispensible for analyzing large plastic deformations, such as deformation after an impact, of thin-walled structures by bending in which the primary deformation mechanism by bending consists of tension and compression across the thin sheets. The proposed high-speed material testing technique can support the computer-aided simulation of micro-forming processes, reliability assessments of micro-products and MEMS products in relation to the strain-rate.

Fig. 1 Material testing results with respect to specimen cross-sectional area at various strain-rates

EXPERIMENTAL TECHNIQUES

The material for the micro-tensile tests in this study was cold-rolled OFHC copper with thickness of 0.1 mm. OFHC copper film was hot-rolled once initially. The number of cold rolling passes is two for OFHC copper film. OFHC copper film was annealed after the first cold rolling process and hard (H04) tempered in the annealing process. OFHC copper consists of 99.99% copper. The dimensions of the micro specimen used here are shown in Fig. 2. The gauge length is 1 mm and the width of the gauge section is 0.2 mm. The overall width is 2 mm and the total length of the specimen is 20 mm. One end of the micro specimen is longer than the other end of the micro specimen, as high-speed tensile tests require a sufficient acceleration distance. The micro specimens were fabricated by micro photo etching, which is a process used in micro-fabrication to remove parts selectively from a thin film or from a bulk substrate. A specimen pattern after micro photo etching is shown in Fig. 3. The micro specimens were prepared for the tensile tests by carefully removing the supporting beams from the micro specimen pattern. SEM images of a fabricated micro specimen confirm the accurate dimensions and fine surface quality, as shown in Fig. 4 (a) and (b). The gauge width measured was 200±1.8 pm in the entire gauge length. The several black spots visible in the SEM image are tiny dust spots; these have a negligible effect on the outcome of the tests.

Fig. 2 Dimension of a micro specimen[unit: mm]

Fig. 3 Specimen pattern fabricated by micro photo etching

Fig. 4 Micro specimen with a gauge width of 200 ^m machined by micro photo etching: (a) full view; (b) magnified view of a side wall of the gauge section

A High-Speed Material Micro-Testing Machine (HSMMTM) was developed to investigate the high strain-rate material properties of micro coupons. The HSMMTM consists of a loading actuator, a gripper and a load measurement system. The developed HSMMTM is shown in Fig. 5. A linear guide block aligns two stages precisely, and the facing surfaces between the two stages are perfectly parallel. A XY stage finally adjusts the vertical and horizontal alignment with a loading actuator.

The nominal strain-rate range for the HSMMTM is from 1/s to 1000/s with regard to a micro specimen proposed with a gauge length of 1 mm. Tensile loading should be applied after the actuator speed reaches a designated constant tensile speed. The actuator for the HSMMTM should have sufficient acceleration that is higher than that of a conventional high-speed material testing machine, as the dimensions of the micro specimen are much smaller than those of a conventional high-speed material testing specimen. Moreover, it is important to achieve the loading speed quickly. To satisfy the acceleration performance, the actuator of an electro-magnetic linear motor was used for the HSMMTM. The electro-magnetic linear motor employed is a servotube actuator (STA2510 model of Copley Co.) with a maximum acceleration of 580 m/s2, a load capacity of 780 N and a maximum speed of 4.2 m/s. In order to verify the performance of this apparatus, the velocity of the cylinder was compared using an input command at velocities of 1 mm/s to 1000 mm/s without a payload, as shown in Fig. 6 (a) to (d). In a severe case, the velocity of the cylinder reaches an input command velocity of 1000 mm/s after approximately 14 ms and a displacement of 6 mm due to the acceleration time.

Fig. 5 High-speed material micro-testing machine developed: (a) a full view; (b) a detailed view

Fig. 6 Displacement curves with respect to the tensile velocity without payload: (a) 1 mm/s; (b) 10 mm/s; (c) 100 mm/s; (d) 1000 mm/s

The gripping mechanism is a slack adapter type, as shown in Fig. 7. In order to achieve a constant velocity during the tests, a special jig was designed to move some distance without loading a specimen and then seize the specimen instantly at the designated speed. A wedge-type clipper grips one end of the micro specimen and the clipper is then inserted into the moving grip, as shown in Fig. 7 (a), (b) and (c). The loading cylinder moves smoothly toward the fixed jig, and the other end of the micro specimen is gripped on the fixed jig, as shown in Fig. 7 (d) and (e). Finally, the actuator moves as much as the acceleration distance in the opposite direction of the tensile direction. The micro high-speed tensile tests start from this initial position. The grip faces are flat and are fastened with M2 bolts. The contact angle between the moving jig and the clipper is 60° to relieve the impact force caused by the high-speed collision.

A load measurement system for the HSMMTM should be carefully designed, as it is one of the most important parts in determining the quality of the stress-strain curves. In a general case, as the strain-rate increases, the load does not transmit with a uniform distribution to the specimen, the jig and the load cell. The load acquired from the load cell subsequently begins to oscillate because the inertia and the stress wave deform parts of the equipment. This phenomenon is termed load ringing [16]. The load ringing phenomenon can be reduced by increasing the natural frequency of the fixed jig or by measuring the load from the specimen directly. For the HSMMTM, the natural frequency of the fixed jig should be increased, rather than the load being measured from the specimen directly, as the size of the micro specimen is too small to attach strain gages onto it. The load cell used in this step is a piezoelectric-type dynamic force sensor, PCB 201B02, with a maximum load capacity of 444.8 N and an upper frequency limit of 90 kHz. Generally, the load ringing characteristics of a jig are enhanced as the mass of the jig decreases and as the stiffness of the jig increases. By removing unnecessary parts from the grip structure and after shortening the length of the jig, the natural frequency of the proposed fixed jig becomes 25,500 Hz, which is nearly four times the natural frequency of a conventional high-speed material testing machine[22]. The load cell was calibrated seven times at the loading speed of 160 N/s in the static UTM. The scale factor was 100.7±0.5 mV/N. The non-linearity of the load cell is about 1% in the full scale.

The strain along a specimen was measured by a non-contact digital image processing technique[23]. Incremental deformation images with a resolution of 144×480 pixels were taken by a high-speed camera, a Phantom V9.1 model, at a frame rate up to 10,000 frames/s. The lens set used was an AF Micro Nikkor 60 mm F2.8D set with extension tubes of 65 mm. The axial strain was manually measured by analyzing images via image processing, which traces particular spots on a specimen. This is shown in Fig. 8. Two particular points in the reduced section were selected as measuring points, and the axial distance between these two points became the initial gauge length, which was approximately 80% of the length of the reduced section. The axial strain is determined by dividing the gauge length increment by the initial gauge length. The measurement error estimated is about 0.7% due to the resolution of the images from the high-speed camera.

Fig. 7 Gripping procedure for HSMMTM: (a) locate a micro specimen on the clipper; (b) fasten the micro specimen to the clipper; (c) insert the clipper with the micro specimen into the moving jig; (d) locate the actuator to initial loading point; (e) fasten the other end of the micro specimen to the fixed jig; (f) Move the actuator to the initial position as much as the acceleration distance

Fig. 8 Sequential deformed shapes of the micro specimen at a strain-rate of 100/s and image tracing results: (a) 0 ms; (b) 0.5 ms; (c) 1.0 ms; (d) 1.5 ms; (e) 2.0 ms; (f) 2.5 ms

Fig. 9 Load and axial strain measured after the onset of the tensile loading for the designated strain-rate: (a) 1/s; (b) 10/s; (c) 100/s

The slope of the axial strain with respect to time, which is the nominal strain-rate, should be kept constant during the tensile test. The axial strain changes during high-speed tensile tests are plotted in Fig. 9 (a) to (c). The axial strain begins to increase after some elapsed time due to a subsequent error caused by a sudden increase in the load, especially for a strain-rate range lower than 10/s. The strain-rates are kept nearly constant after some elapsed time for a strain-rate range that exceeds 10/s, while the strain-rate increases to 3/s for a designated strain-rate of 1/s. The load ringing phenomenon arises at a strain-rate of 100/s, but the load ringing frequency is 25,500 Hz and the amplitude of oscillation is negligible compared to the measured load response. Stress-strain curves were obtained by synchronizing the axial strain measured via digital image processing and the load from the load cell. It is difficult to synchronize these two measurements at high strain-rates since those are measured from different devices. The strain was tracked by analyzing the camera images. And the strain data points are interpolated to match the number of load data points. Therefore, the error from this synchronization was estimated as the relative frame rate of the high-speed camera used in the process. The frame rate of the camera was 10,000 frames/s and the incremental time was 0.1 msec. The maximum synchronization error is estimated to be a strain of 0.01 at a strain-rate of 100/s.

RATE-DEPENDENT MATERIAL PROPERTIES OF OFHC COPPER FILM

Accurate tensile properties of thin films were obtained at high strain-rates from the developed HSMMTM. The OFHC copper film was tested using a quasi-static testing machine and a high-speed material testing machine at various strain-rates. A micro tester [13] and the developed HSMMTM were used for the tensile tests. The reduced section of a micro specimen had a length of 1 mm and a width of 0.2 mm. The rate-dependent stress-strain curves of the OFHC copper film are shown in Fig. 10 (a). Tests were conducted twice for each condition, and three times if the results were not reproducible. The stress-strain curves obtained here confirmed that the flow stress and the strain hardening increase as the strain-rate increases. The yield stress at a strain-rate of 100/s was 247.7 MPa, which is 19.3% higher than that at a strain-rate of 0.001/s, 288.6 MPa. Fig. 10 (b) illustrates the variation of the strain-rate sensitivity, indicating the variation of the flow stress with respect to the strain-rate with variation of the strain. The curve marked with square symbols denotes the initial yield stress curve; the subsequent curves denote the flow stress curves according to the corresponding plastic strain. The interval between the symbols under the same strain-rate indicates the amount of strain hardening. For the OFHC copper film in Fig. 10 (b), the yield stress at a strain-rate of 100/s is 19.3% higher than that at a strain-rate of 0.001/s while the flow stress at a plastic strain of 0.075 at a strain-rate of 100/s is 26.4% higher than that at a strain-rate of 0.001/s. Thus, the strain hardening becomes larger as the strain-rate increases. This phenomenon was explained by Follansbee and Kocks [26] and Tong et al. [27]. Tong et al. demonstrated that this strain-rate dependence of strain hardening in copper arises due to the increasing difficulty of dislocations to overcome obstacles at high strain-rates, leading to an increased multiplication rate and to an increase in the strain-rate sensitivity of strain hardening.

Fig. 10 (c) shows the fracture elongation of the OFHC copper film with respect to the logarithmic scale of the strain-rate. The fracture elongation increases as the strain-rate increases from 0.001 to 0.1/s and then decreases slightly at a strain-rate of 1/s before increasing again to 100/s. Rate-dependent fracture elongations of conventional steel sheets also show similar tendencies in that ductility of TRIP600 and DP600 steels does not decrease as the strain-rates increase [28-30]. The fracture elongation of the OFHC copper film at a strain-rate of 0.001/s is 11.4% while the fracture elongation at a strain-rate of 100/s is 23.4%, which is an increase of 105.3% compared to the quasi-static case. Strain hardening has critical effects on the fracture elongation. The final shapes of micro specimens were shown in Fig. 11.

Fig. 10 Rate-dependent material properties of the OFHC copper film: (a) engineering stress-strain curves; (b) strain-rate sensitivity; (c) fracture elongation

Fig. 11 Micro specimens after the fracture

CONCLUSION

A High-Speed Material Micro-Testing Machine (HSMMTM) was newly developed for the high-speed material testing of thin films at strain-rates ranging from 1/s to 500/s. The proposed HSMMTM utilizes a high-performance electro-magnetic servo actuator. A fixed grip with a ring-type load cell reduces the load ringing phenomenon effectively. A slack adapter type gripping mechanism was designed to seize the micro specimen instantly after the designated tensile speed was reached.

Micro specimens with a gauge length of 1 mm were fabricated by a micro photo etching technique, showing a good surface quality along with good dimensional accuracy. The rate-dependent material properties of an OFHC copper film with a thickness of 0.1 mm were evaluated at strain-rates that ranged from 1/s to 500/s using the developed HSMMTM. The stress-strain curves of the OFHC copper film show positive strain-rate sensitivity and the strain hardening gradually increases as the strain-rate increase. The strain-hardening increase with the increase in the strain-rate increases the fracture elongation with respect to the strain-rate. Experimental results of an OFHC copper film provide rate-dependent flow stress curves and fracture elongation values, which are indispensable mechanical properties that can be used to analyze the micro-forming process and can be used as part of a structural analysis of micro-parts in conjunction with a numerical simulation.